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If f(x) = 4^x-8 and g(x) = 5x+6, find (f + g)(x)
A. (F+g)(x) = -4^x - 5x + 2
B.(F+g)(x) = 4^x + 5x - 2
C.(F+g)(x) = 4^x - 3x + 6
D.(F+g)(x) = 9x - 2

Respuesta :

VectorFundament120

Hey there!

We are given two functions - one is Exponential while the another one is Linear.

[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]

1. Operation of Function

  • (f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:

[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]

2. Substitution

  • Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.

[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]

3. Evaluate/Simplify

  • Cancel out the brackets and combine like terms.

[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]

4. Final Answer

  • (f+g)(x) = 4^x+5x-2

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